leveraging functional annotations in genetic risk ...€¦ · research article leveraging...

RESEARCH ARTICLE

Leveraging functional annotations in genetic

risk prediction for human complex diseases

Yiming Hu1☯, Qiongshi Lu1☯, Ryan Powles2, Xinwei Yao3, Can Yang4, Fang Fang1,

Xinran Xu1, Hongyu Zhao1,2,5,6*

1 Department of Biostatistics, Yale School of Public Health, New Haven, CT, United States of America,

2 Program of Computational Biology and Bioinformatics, Yale University, New Haven, CT, United States of

America, 3 Yale College, New Haven, CT, United States of America, 4 Department of Mathematics, Hong

Kong Baptist University, Kowloon, Hong Kong, 5 Department of Genetics, Yale University School of

Medicine, New Haven, CT, United States of America, 6 Clinical Epidemiology Research Center (CERC),

Veterans Affairs (VA) Cooperative Studies Program, VA Connecticut Healthcare System, West Haven, CT,

United States of America

☯ These authors contributed equally to this work.

* [email protected]

Abstract

Genetic risk prediction is an important goal in human genetics research and precision medi-

cine. Accurate prediction models will have great impacts on both disease prevention and

early treatment strategies. Despite the identification of thousands of disease-associated

genetic variants through genome wide association studies (GWAS), genetic risk prediction

accuracy remains moderate for most diseases, which is largely due to the challenges in

both identifying all the functionally relevant variants and accurately estimating their effect

sizes in the presence of linkage disequilibrium. In this paper, we introduce AnnoPred, a prin-

cipled framework that leverages diverse types of genomic and epigenomic functional anno-

tations in genetic risk prediction for complex diseases. AnnoPred is trained using GWAS

summary statistics in a Bayesian framework in which we explicitly model various functional

annotations and allow for linkage disequilibrium estimated from reference genotype data.

Compared with state-of-the-art risk prediction methods, AnnoPred achieves consistently

improved prediction accuracy in both extensive simulations and real data.

Author summary

Genetic risk prediction plays a significant role in precision medicine. Accurate prediction

models could have great impact on disease prevention and early treatment strategies. For

example, mutations in BRCA1 and BRCA2 have been used to evaluate women’s breast

cancer risk and as a guideline for early screening. However, genetic risk prediction models

also present important challenges, including extreme high-dimensionality, limited access

to and efficient computational methods for individual-level genotype data. To make use

of rich GWAS summary statistics, we propose a novel method to address these challenges

by integrating genomic functional annotations, which have been successfully applied in

GWAS to generate biological insights. We demonstrate the improvement in accuracy in

PLOS Computational Biology | https://doi.org/10.1371/journal.pcbi.1005589 June 8, 2017 1 / 16

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OPENACCESS

Citation: Hu Y, Lu Q, Powles R, Yao X, Yang C,

Fang F, et al. (2017) Leveraging functional

annotations in genetic risk prediction for human

complex diseases. PLoS Comput Biol 13(6):

e1005589. https://doi.org/10.1371/journal.

pcbi.1005589

Editor: Isidore Rigoutsos, Thomas Jefferson

University, UNITED STATES

Received: October 21, 2016

Accepted: May 19, 2017

Published: June 8, 2017

Copyright: © 2017 Hu et al. This is an open access

article distributed under the terms of the Creative

Commons Attribution License, which permits

unrestricted use, distribution, and reproduction in

any medium, provided the original author and

source are credited.

Data Availability Statement: All the GWAS

summary statistics are available online and can be

accessed through: http://www.ibdgenetics.org,

http://gameon.dfci.harvard.edu, http://www.

broadinstitute.org/ftp/pub/rheumatoid_arthritis/

Stahl_etal_2010NG/, http://diagram-consortium.

org/downloads.html and https://www.

immunobase.org/downloads/protected_data/

GWAS_Data/. Individual level genotype data are

available from dbGaP (accession numbers:

phs000147, phs000383, phs000237 and

phs000274) and WTCCC on EGA https://www.ebi.

https://doi.org/10.1371/journal.pcbi.1005589

http://crossmark.crossref.org/dialog/?doi=10.1371/journal.pcbi.1005589&domain=pdf&date_stamp=2017-06-22








http://creativecommons.org/licenses/by/4.0/

http://creativecommons.org/licenses/by/4.0/

http://www.ibdgenetics.org

http://gameon.dfci.harvard.edu

http://www.broadinstitute.org/ftp/pub/rheumatoid_arthritis/Stahl_etal_2010NG/



http://diagram-consortium.org/downloads.html

http://diagram-consortium.org/downloads.html

https://www.immunobase.org/downloads/protected_data/GWAS_Data/



https://www.ebi.ac.uk/ega/

both extensive simulation studies and real data analysis of breast cancer, Crohn’s disease,

celiac disease, rheumatoid arthritis and type-II diabetes.

This is a PLOS Computational Biology Methods paper.

Introduction

Achieving accurate disease risk prediction using genetic information is a major goal in human

genetics research and precision medicine. Accurate prediction models will have great impacts

on disease prevention and early treatment strategies [1]. Advancements in high-throughput

genotyping technologies and imputation techniques have greatly accelerated discoveries in

genome-wide association studies (GWAS) [2]. Various approaches that utilize genome-wide

data in genetic risk prediction have been proposed, including machine-learning models

trained on individual-level genotype and phenotype data [3–8], and polygenic risk scores

(PRS) estimated using GWAS summary statistics [9, 10]. Despite the potential information

loss in summary data, PRS-based approaches have been widely adopted in practice since the

summary statistics for large-scale association studies are often easily accessible [11, 12] while

individual-level data are more difficult to acquire, deposit, and process. However, prediction

accuracies for most complex diseases remain moderate, which is largely due to the challenges

in both identifying all the functionally relevant variants and accurately estimating their effect

sizes in the presence of linkage disequilibrium (LD) [13].

Explicit modeling and incorporation of external information, e.g. pleiotropy [7, 8] and LD

[10], has been shown to effectively improve risk prediction accuracy. Recent advancements in

integrative genomic functional annotation, coupled with the rich collection of summary statis-

tics from GWAS, have enabled increase of statistical power in several different settings [14–

16]. To our knowledge, the impact of functional annotations on performance of genetic risk

prediction has not been systematically studied. Here, we introduce AnnoPred (available at

https://github.com/yiminghu/AnnoPred), a principled framework that integrates GWAS sum-

mary statistics with various types of annotation data to improve risk prediction accuracy. We

compare AnnoPred with state-of-the-art PRS-based approaches and demonstrate its consis-

tent improvement in risk prediction performance using both simulations and real data of mul-

tiple complex diseases.

AnnoPred risk prediction framework has three main stages (Methods). First, we estimate

GWAS signal enrichment in 61 different annotation categories, including functional genome

predicted by GenoCanyon scores [17], GenoSkyline tissue-specific functionality scores of 7

tissue types [14], and 53 baseline annotations for diverse genomic features [18] for each trait

analyzed. Second, we propose an empirical prior of SNP effect size based on annotation assign-

ment and signal enrichment. In general, SNPs located in annotation categories that are highly

enriched for GWAS signals receive a higher effect size prior. Finally, the empirical prior is

adopted in a Bayesian framework in which marginal summary statistics and LD matrix esti-

mated from a reference panel are jointly modeled to infer the posterior effect size of each SNP.

AnnoPred PRS is defined by

PRS ¼XM

j¼1

XjEAðbjjb; DÞ

Leverage annotations in risk prediction


ac.uk/ega/ (accession numbers:

EGAD00000000001, EGAD00000000002,

EGAD00000000007 and EGAD00001000401).

Funding: This study was supported in part by the

National Institutes of Health (https://www.nih.gov/)

grants R01 GM59507, the VA Cooperative Studies

Program of the Department of Veterans Affairs,

Office of Research and Development (http://www.

research.va.gov/programs/csp/), and the Yale

World Scholars Program (http://bbs.yale.edu/

training/initiatives/csc.aspx) sponsored by the

China Scholarship Council. The funders had no role

in study design, data collection and analysis,

decision to publish, or preparation of the

manuscript.

Competing interests: The authors have declared

that no competing interests exist.

https://github.com/yiminghu/AnnoPred


https://www.ebi.ac.uk/ega/

https://www.nih.gov/

http://www.research.va.gov/programs/csp/

http://www.research.va.gov/programs/csp/

http://bbs.yale.edu/training/initiatives/csc.aspx

http://bbs.yale.edu/training/initiatives/csc.aspx

where Xj and βj are the standardized genotype and effect size of the jth SNP, respectively, b is

the marginal estimate of β, D is the sample LD matrix, and EAðbjjb; DÞ denotes the posterior

expectation of effect sizes under an empirical prior based on annotation assignment for all

SNPs when adjusting for LD matrix estimated from a reference panel (Methods).

Results

We first performed simulations to demonstrate AnnoPred’s ability to improve risk prediction

accuracy. We compared AnnoPred with four popular PRS approaches (Methods), including

PRS based on genome-wide significant SNPs (PRSsig), PRS based on all SNPs in the dataset

(PRSall), PRS based on tuned cutoffs for p-values and LD pruning (PRSP+T), and recently pro-

posed LDpred [10]. Mean correlations between simulated and predicted traits were calculated

from 100 replicates under different simulation settings (Methods). AnnoPred showed the best

prediction performance in all settings when the causal SNPs are highly enriched in annotated

regions (Table 1, S2 Table and S2 Fig). In general, performance of PRSsig, PRSP+T, LDpred,

and AnnoPred all improved under a sparser genetic model and higher trait heritability. PRSall

showed comparable performance between sparse and polygenic models but its prediction

accuracy was consistently worse than other methods. Sample size in the training set was also

crucial for risk prediction accuracy. Increasing sample size could lead to continuous improve-

ment in prediction accuracy under different settings (Fig 1).

To illustrate the improved risk prediction performance in real data, we applied AnnoPred

to five human complex diseases—Crohn’s disease (CD), breast cancer (BC), rheumatoid ar-

thritis (RA), type-II diabetes (T2D), and celiac disease (CEL). We first estimated GWAS signal

enrichment in different annotation categories (Methods). Enrichment pattern varies greatly

across diseases (Fig 2A; S1 Table), reflecting the genetic basis of these complex phenotypes.

Functional genome predicted by GenoCanyon was consistently and significantly enriched

for all five diseases. Blood was strongly enriched for three immune diseases, namely CD (P =

8.9×10−12), CEL (P = 7.0×10−15), and RA (P = 9.9×10−6), while gastrointestinal (GI) tract was

enriched in CD (P = 2.6×10−5) and CEL (P = 1.4×10−4), both of which have a known GI com-

ponent. For BC, epithelium (P = 7.4×10−4), GI (P = 5.9×10−3), and muscle (P = 6.1×10−3) were

significantly enriched. A few studies have shown that breast cancer could arise from epithelial

cells [19, 20]. The connections between breast cancer and muscle as well as GI tract have also

been previously suggested [21, 22]. In addition, studies have suggested that GI can be used as

Table 1. Mean correlation between simulated and predicted traits calculated from 100 replicates under different simulation settings. The highest

mean correlations are highlighted in boldface. Standard deviations are shown in parentheses. Traits were simulated from WTCCC genotype data, which con-

tain 15,918 individuals genotyped for 393,273 SNPs. In each setting, we used 70% of the data to calculate the training summary statistics and randomly

divided the rest 30% into two parts for parameter tuning.

Training samples Heritability #Causal PRSsig PRSall PRSP+T LDpred AnnoPred

Half (~5K) 0.25 300 0.149(.028) 0.08(.021) 0.25(.028) 0.279(.025) 0.286(.024)

3000 NA* 0.082(.016) 0.073(.020) 0.087(.019) 0.096(.020)

0.5 300 0.304(.04) 0.16(.022) 0.48(.026) 0.502(.033) 0.512(.026)

3000 NA* 0.157(.019) 0.157(.024) 0.195(.021) 0.209(.019)

Full (~10K) 0.25 300 0.217(.031) 0.11(.02) 0.332(.023) 0.35(.033) 0.358(.022)

3000 NA* 0.11(.014) 0.107(.018) 0.136(.017) 0.145(.017)

0.5 300 0.373(.036) 0.213(.023) 0.548(.024) 0.557(.047) 0.566(.034)

3000 0.078(.023) 0.21(.019) 0.243(.021) 0.309(.021) 0.324(.019)

* NA means no SNP achieves genome-wide significance level (5e-8).

https://doi.org/10.1371/journal.pcbi.1005589.t001





diagnostic and treatment target for type-II diabetes, Crohn’s disease, and celiac disease [23–

25]. Furthermore, the connection between immune system and Crohn’s disease, celiac disease

and rheumatoid arthritis have been extensively studied in literature [26–28]. Next, we evalu-

ated the effectiveness of proposed empirical effect size prior in three diseases (i.e. CD, CEL,

and RA) with well-powered testing cohorts (N>2,000). Interestingly, despite the highly vari-

able enrichment results in training datasets, integrative effect size prior could effectively iden-

tify SNPs with large effect sizes and consistent effect directions in independent validation

cohorts (Fig 2B and 2C).

Correlations between the calculated PRS and disease status (COR) for different approaches

are summarized in Table 2. AnnoPred showed consistently improved prediction accuracy

compared with all other methods across five diseases. Notably, PRSsig and PRSall showed sub-

optimal performance in these datasets, reaffirming the importance of modeling LD and other

external information. A likelihood ratio test was used to test for the difference in the prediction

accuracy between models comparing the likelihood of a logistic regression fitting PRS of one

method to that of a logistic regression fitting PRS of two methods jointly (S11 Table). From

the test, AnnoPred with 61 annotations performed significantly better than LDpred (p = 1.2E-

22 for CD, p = 0.045 for BC, p = 4.2E-7 for RA, p = 3.3E-4 for T2D and p = 1.3E-3 for CEL).

Reversing the order of test (that is, comparing the likelihood of model using annotations with

Fig 1. Evaluating the effect of sample size on prediction accuracy in simulation. Traits were simulated

using SNPs of chromosome 1, chromosome 1 and 2, chromosome 1 to 4 and the whole genome while

keeping the same proportion of causal variants and heritability to mimic the situation of increasing sample

size. In the figure, logNr = logN MMs

, where N is the number of individuals, M is the total number of variants and

Ms is the number of variants used in simulation. In total four settings were simulated for each effective sample

size: h2 = 0.25, p = 0.001; h2 = 0.25, p = 0.01; h2 = 0.5, p = 0.001; h2 = 0.5, p = 0.01, where p represents the

proportion of causal variants. Each dot represent the mean COR of 50 replicates in one simulation setting and

error bar represents the standard error.

https://doi.org/10.1371/journal.pcbi.1005589.g001





model using and not using annotations jointly) results in non-significant p-values for most

tests (S11 Table), which further demonstrates that PRS incorporating functional annotations

mostly encompasses the information of PRS without annotations. To test different methods’

ability to stratify individuals with high risk, we compared the proportion of cases among test-

ing samples with high PRS. AnnoPred outperformed all other methods in CD, CEL, RA, and

T2D (S1 Fig). Next, we tested AnnoPred’s performance using only the 53 baseline annotations

and observed a substantial drop in prediction accuracy for all diseases (S3 Table). AnnoPred

with GenoCanyon and GenoSkyline annotations only (nine annotation tracks in total) yields

better performance than the 53 baseline annotations (S10 Table). For CD and T2D, by using

Fig 2. Evaluating effectiveness of annotations and empirical effect size prior. (A) GWAS signal enrichment across GenoCanyon and tissue-specific

GenoSkyline annotations. The horizontal lines mark p-value cutoffs of 0.05 and Bonferroni corrected significance level. (B) Comparing signal strength

of SNPs with high priors and low priors in independent validation cohorts. SNPs with higher priors have significantly stronger associations across three

independent and well-powered testing datasets (N>2,000). P-values were calculated using one-sided Kolmogorov-Smirnov test. (C) Comparing consistency of

SNPs’ effect direction between training and testing datasets. Each bar quantifies the proportion of SNPs with consistent effect directions. P-values were

calculated using one-sided two-sample binomial test.


Table 2. CORs of different methods. The highest CORs are highlighted in boldface.

Disease/Trait PRSsig PRSall PRSP+T LDpred AnnoPred

Crohn’s Disease 0.27 0.229 0.32 0.325 0.343

Breast Cancer 0.084 0.055 0.12 0.122 0.137

Rheumatoid Arthritis 0.204 0.114 0.248 0.282 0.287

Type-II Diabetes 0.165 0.156 0.204 0.202 0.22

Celiac Disease 0.11 0.136 0.18 0.197 0.213







these 9 categories AnnoPred even achieved higher accuracy than the model with all 61 annota-

tion tracks added. These results highlight the importance of annotation quality in genetic risk

prediction, and also demonstrate GenoCanyon and GenoSkyline’s ability to accurately identify

functionality in the human genome. Since different diseases have various enrichment patterns,

we also run AnnoPred with significantly enriched annotations (enrichment test p value less

than 0.05) for each disease (S10 Table). In general, using only the significantly enriched anno-

tations indeed improved the performance in most diseases.

Tissue specificity plays an important role in genetic risk prediction. Integrating more func-

tional annotations with higher tissue and cell type specificity may further increase risk predic-

tion accuracy, especially when the tissue type that is biologically relevant to the disease is not

well characterized by the seven available tissue tracks in our current analyses. To explore how

these factors will affect the AnnoPred model, we performed a few follow-up analyses. We have

recently expanded our GenoSkyline annotations to more than 100 tissue and cell types from

the Roadmap Epigenomics Project [29]. We investigated the performance of AnnoPred after

integrating 66 annotation tracks representing a spectrum of adult tissue and cell types. As

shown in S10 Table, incorporating more annotations into the model does not always further

improve risk prediction accuracy compared with AnnoPred with fewer annotations in the

model. This may be due to the overlap between functional regions (e.g. functional annotations

for slightly different brain regions) when incorporating too many annotation tracks into the

model, which will cause numerically unstable heritability estimates. This is because annota-

tion-stratified LD score regression, the method we used to empirically estimate the informative

prior for SNPs’ effect sizes, is a multiple linear regression model that regresses SNP-level sum-

mary statistics against annotation-stratified LD scores. When two functional annotation tracks

are similar, the corresponding LD scores will also be correlated by definition. It is well under-

stood that if multi-collinearity (i.e. correlation among covariates) in multiple regression leads

to numerically unstable estimates for regression coefficients [30] (the heritability parameters

in our case).

In order to study the effect of highly associated SNPs (e.g. SNPs in MHC regions for

immune traits), we repeated the analysis on CD, RA, BC and T2D after removing the SNPs in

MHC region (chr6: 28,477,797–33,448,354 bp). Re-analysis of CEL was unnecessary since the

training summary statistics of CEL does not contain any SNP in the MHC region. After

removing SNPs in MHC regions, the prediction accuracies for RA drops dramatically for all

methods and AnnoPred remained to be the method with the best performance (S9 Table). For

the rest diseases, results varied little from the original analysis. Besides COR, we also included

AUCs for all the analysis performed (S2, S6, S9 and S10 Tables), all of which showed consis-

tent patterns.

Due to distinct allele frequencies and LD structures across populations, risk prediction

accuracy usually drops when the training and testing samples are from different populations.

In order to investigate the robustness of AnnoPred against population heterogeneity, we

applied AnnoPred to three non-European cohorts for breast cancer and type-II diabetes while

training the model using summary statistics from European-based studies. The CORs and

AUCs are summarized in S6 and S7 Tables. As expected, we observed a drop in prediction

accuracy for all methods. However, AnnoPred still performed the best in all three trans-ethnic

validation datasets.

Discussion

Our work demonstrates that functional annotations can effectively improve performance of

genetic risk prediction. AnnoPred jointly analyzes diverse types of annotation data and GWAS




summary statistics to upweight SNPs with a higher likelihood of functionality, which lead to

consistently better prediction accuracy for multiple complex diseases. Our method is not with-

out limitation. First, despite the consistent improvement compared with existing PRS-based

methods, accuracies for most diseases remain moderate. In order to effectively stratify risk

groups for clinical usage, our model remains to be further calibrated using large cohorts with

measured environmental and clinical risk factors [1]. Second, accurate estimation of GWAS

signal enrichment and SNP effect sizes requires a large sample size for the training dataset.

This could potentially be improved by new estimators for annotation-stratified heritability

[19]. A few Bayesian models combining GWAS summary statistics with functional annota-

tions have been proposed for the purpose of fine-mapping functional variants [16, 20, 21].

Whether these models could be adapted to benefit risk prediction accuracy remains to be

investigated in the future. Importantly, the rich collection of publicly available integrative

annotation data, in conjunction with the increasing accessibility of GWAS summary statistics,

makes AnnoPred a customizable and powerful tool. As GWAS sample size continues to grow,

AnnoPred has the potential to achieve even better prediction accuracy and become widely

adopted as a summary of genetic contribution in clinical applications of risk prediction.

Methods

Annotation data

GenoCanyon is a statistical framework to predict functional regions in the human genome

through integrative analysis of ENCODE epigenomic data and multiple conservation metrics

[17]. Later we have further extended the model and developed GenoSkyline, which aimed to

predict tissue-specific functionality [14]. In the AnnoPred model, we incorporated GenoCan-

yon general functionality scores, GenoSkyline tissue-specific functionality scores for seven tis-

sue types (brain, gastrointestinal tract, lung, heart, blood, muscle, and epithelium), and 53

LDSC baseline annotations that covered a variety of genomic features [18] (S1 Table). We

smoothed GenoCanyon scores by a 10Kb window, a strategy previously shown to improve

robustness of functionality prediction [22]. The smoothed GenoCanyon annotation and raw

GenoSkyline annotations of seven tissue types were dichotomized based on a cutoff of 0.5. The

regions with GenoCanyon or GenoSkyline scores greater than the cutoff were interpreted as

non-tissue-specific or tissue-specific functional regions in the human genome. Such dichoto-

mization has been previously shown to be robust against the cutoff choice [14]. Notably, the

AnnoPred framework allows users to specify their own choice of annotations.

Heritability partition

We assume throughout the paper that both the phenotype YN×1 and the genotypes XN×M are

standardized with mean zero and variance one. We assume a linear model

YN�1 ¼ XN�MbM�1 þ εN�1

X, β and ε are mutually independent. We also assume that β is a random effect and effects of

different SNPs are independent. A key idea in the AnnoPred framework is to utilize functional

annotation information to accurately estimate SNPs’ effect sizes. In order to achieve that, we

first partition trait heritability by annotations using LD score regression [18]. Since genotypes

are standardized, per-SNP heritability is defined as the variance of βi for the ith SNP, and is

used to quantify SNP effect sizes. More specifically, assume there are K + 1 pre-defined annota-

tion categories, denoted as S0, S1, . . ., SK with S0 representing the entire genome. Under an

additive assumption for heritability in overlapped annotations, we have bi � Nð0;P

j:i2SjtjÞ,




where τ0, τ1, . . ., τK, quantify the contribution to per-SNP heritability from each annotation

category. Denote the estimated marginal effect size of the ith SNP as bi ¼XTi YN , then we have the

following approximation

EðNb2

i Þ � ðN � 1ÞX

k

tklði; kÞ þ 1

where l(i, k) is the annotation-stratified LD score and N denotes the total sample size. Regres-

sion coefficients τk are estimated through weighted least squares. The estimated heritability of

the ith SNP is then dVar ðbiÞ ¼P

j:i2Sjt j.

Empirical prior of effect size

Based on per-SNP heritability estimates, we propose two different priors for SNP effect sizes to

add flexibility against different genetic architecture. For the first prior, we assume that SNP

effect size follows a spike-and-slab distribution

bi � p0N 0; s2

i

�

p0

� �þ 1 � p0ð Þd0

where p0 is the proportion of causal SNPs in the dataset, and δ0 is a Dirac function representing

a point mass at zero. The empirical variance of each SNP, i.e. s2i , is determined by the annota-

tion categories it falls in. More specifically, we assume s2i ¼ cð

Pj:i2Sj

t jÞ, where c is a constant

calculated from the following equation

Pis

2

i ¼ H 2:

We do not directly useP

j:i2Sjt j as the empirical variance prior because it is estimated in the

context where all SNPs in the 1000 Genomes Project database are included in the model [18].

Such per-SNP heritability estimates cannot be extrapolated to the risk prediction context

where many fewer SNPs are analyzed [23]. Therefore, we rescale the heritability estimates to

better quantify each SNP’s contribution toward chip heritability. Following [24], we use a sum-

mary statistics-based heritability estimator that approximates the Haseman-Elston estimator:

H 2 ¼ð�w2 � 1Þ

N�l

where �w2 and�l denote the mean Nb2i and mean non-stratified LD score, respectively.

In the first prior, we assumed the same proportion of causal SNPs but different effect sizes

across annotation categories. We now describe the second prior that assumes different propor-

tions of causal SNPs but the same effect size across annotation categories. To be specific, we

assume the causal effect size to be Var(β causal) = V, the total number of SNPs to be M0, and the

overall proportion of causal SNPs to be p0. The total heritability H20

can then be written as

H20¼ p0M0V . For the ith SNP, use Ti ¼ ð

Tj:i2Sj

SjÞ \ ðT

k:i=2SkSckÞ to denote the collection of

SNPs that share the same annotation assignment with the ith SNP, and let MTi¼ jTij, i.e. the

number of SNPs in the set. Then, the total heritability of SNPs in Ti is H2Ti¼ pTi

MTiV , with pTi

denoting the proportion of causal SNPs in Ti. Following these notations, we have

bi � pTiNð0;VÞ þ ð1 � pTi

Þd0

where V ¼ H0

p0N0and pTi

¼ p0

M0H2Ti

MTiH20

. We use H 2 to estimate H20, and the following formula to




estimate H2Ti

.

H 2

Ti¼

Pk2Ti

Pj:k2Sj

t jPM0

k¼1

Pj:k2Sj

t j

H 2

Finally, p0 is treated as a tuning parameter for both prior functions in our analysis.

Calculation of posterior effect sizes

By Bayes’ rule, the posterior distribution of β is:

f ðbjb; DÞ / f ðbjb; DÞf ðbÞ

where D ¼ 1

N XTX is the sample correlation matrix and b ¼ 1

N XTY is the marginal effect size

estimates. Given β and D, b follows a multivariate normal distribution asymptotically with the

following mean and variance

E bjb; D� �

¼1

NEðXTXbjb; DÞ þ EðXTεjb; DÞ� �

¼ Db

Var bjb; D� �

¼ Var1

NXTεjb; D

� �

¼1

N1 � h2

g

� �D:

However, D is usually non-invertible and has very high dimensions. We thus study the pos-

terior distribution of a small chunk of b instead. Let bb be the estimated marginal effect size of

SNPs in a region b (e.g. a LD block) and the corresponding genotype matrix is Xb and sample

correlation matrix is Db. Then the conditional mean and variance of bb are

E bbjbb; Db

� �¼

1

NEðXT

b Xbjbb; DbÞ þ EðXTb εjbb; DbÞ

� �¼ Dbbb

Var ðbb jbb; DbÞ ¼1

N2varðXT

b Xbbb þ XTb ðX� bb� b þ εÞjbb; DbÞ

¼1

N2varðXT

b ðX� bb� b þ εÞjbb; DbÞ

¼1

N2XT

b varðX� bb� b þ ε jbb; DbÞXb

¼1

Nð1 � h2

bÞDb

where h2b ¼

Pi2b s2

i is the heritability of SNPs in region b, and X−b and β−b denote the genotype

matrix and effect sizes of SNPs not in region b. The conditional distribution of βb is:

f ðbb jbb; DbÞ / N Dbbb;1

Nð1 � h2

bÞDb

� �Q

i2bf ðbiÞ

/

(N Dbbb;

1

Nð1 � h2

bÞDb

� �Q

i2bp0N 0; s2

i

�

p0

� �þ ð1 � p0Þd0

h i; under the first prior

N Dbbb;1

Nð1 � h2

bÞDb

� �Q

i2b½pTi

Nð0;VÞ þ ð1 � pTiÞd0�; under the second prior




Although it is difficult to derive Eðbbjbb; DbÞ from the joint conditional distribution of βb,

each element of βb follows a mixed normal distribution conditioning on bb, Db, and all other

elements in βb. Therefore, we apply a Gibbs sampler to draw samples from f ðbbjbb; DbÞ and

use the sample mean as an approximation for Eðbbjbb; DbÞ. We further performed a sensitivity

analysis on the choice of the size of block b (S6 Fig). Specifically, we ran AnnoPred on the data

of Crohn’s disease with different sizes of block and found that the results were robust to the

sizes. In practice, the size of block b is specified by the total number of variants divided by

3,000.

Calculation of PRS

PRS is calculated using the following formula

PRS ¼PM

j¼1XjEAðbjjb; DÞ;

where EA denotes the posterior expectation as described above. In practice, the individual-level

genotype matrix is not available and we use the LD matrix estimated from a reference panel or

the validation samples to substitute D. We apply the same standard of choosing the size of b as

described in [10]. Choices of prior and p0 can be tuned in an independent cohort. For the data

analysis described in this work, we adopted a cross-validation scheme to select tuning parame-

ter due to the challenge in finding multiple independent cohorts without overlapping with the

training GWAS summary statistics. The training datasets in our real data analyses and simula-

tions are always fixed, i.e. GWAS summary statistics. We did not perform a classical cross-vali-

dation by using different subsets of the complete data to train and test our prediction model.

The purpose of cross-validation in our study is purely parameter tuning. To select a suitable

tuning parameter, we divide the independent testing dataset (individual level genotype and

phenotype data) into two equal parts (A and B), and select the tuning parameters by optimiz-

ing prediction accuracy on dataset A. We then evaluate prediction accuracy using the remain-

ing half of testing data, i.e. dataset B. Finally, we repeat the analysis one more time by choosing

the tuning parameter on dataset B while evaluating the prediction accuracy on dataset A.

Results from these two separate analyses are averaged to quantify model performance. For

T2D where multiple independent cohorts are available (phs000237 and phs000388), we used

an independent cohort for parameter tuning and the other for evaluating performance (S12

Table). The results are consistent with the cross-validation.

Comparison with existing methods

We compared AnnoPred with several commonly used risk prediction methods based on sum-

mary data of association studies. PRSsig and PRSall were both calculated as the inner product of

marginal effect size estimates and the corresponding genotypes. PRSall used all the SNPs that

are shared between training and testing datasets while PRSsig only used SNPs with p-values

below 5 × 10−8 in the training set. PRSP+T used SNPs passing both LD pruning and p-value

thresholding. The thresholds are tuned in an independent dataset over a grid (0, 0.1, 0.2, . . .

0.9 for LD; 1, 0.3, 0.1, 0.03, 0.01, 3E-3, 1E-3, 3E-4, 1E-4, 3E-5, 1E-5, 1E-6, 1E-7, 5E-8, 1E-8 for

p-value). LDpred can be viewed as a special case of AnnoPred, assuming the whole genome as

the only functional annotation. This is because when enrichment is constant (i.e. causal vari-

ants are uniformly distributed across the genome), per-SNP heritability estimates would be

nearly constant and therefore results in similar performance to LDpred. We have performed

an additional simulation to demonstrate this using WTCCC genotype data with ~15K individ-

uals and ~330K variants. We randomly divided the genome into two parts (two annotations)




and uniformly selected causal SNPs. Then the traits were simulated in a similar way as other

simulations in this paper. We estimated per-SNP heritability using LDSC in the two annota-

tion categories, respectively. We ran the procedure for 100 times and the distributions of esti-

mated per-SNP heritability in both regions are summarized in the figure below (the dashed

line denotes the true per-SNP heritability, added as S4 Fig in the manuscript), which indicates

that the per-SNP heritability estimates are uniform across the genome under constant enrich-

ment. Therefore, AnnoPred would be mathematically equivalent with LDpred with enrich-

ment is constant. We downloaded python code for PRSP+T and LDpred from Github (https://

github.com/bvilhjal/ldpred). All the tuning parameters were tuned through cross-validation as

we did for AnnoPred. Besides all these PRSs, we also compared AnnoPred with a evaluating

method used in [5], which uses 1E-1, 1E-2,. . ., 1E-5 as p-value threshold to select SNPs and

report the accuracy for the best performed threshold (S4 and S5 Tables).

Given that many large-scale GWAS summary statistics have included almost all available

cohorts for a disease of interest, it is challenging to find independent datasets with individual-

level genotype and phenotype information and sufficient sample sizes. We were able to identify

ideal validation datasets for the five diseases we analyzed in this paper. The performance of dif-

ferent methods on more traits shall be evaluated when we get access to more data in the future.

Simulation settings

We simulated traits from WTCCC genotype data, which contain 15,918 individuals genotyped

for 393,273 SNPs after filtering variants with missing rate above 1% and individuals with

genetic relatedness above 0.05. We first generated two annotations and each annotation was

simulated by randomly selecting 10% of the genome, denoted as A1 and A2, which we assume

are known when applying AnnoPred. Denote the heritability of the trait as h2g (25% or 50%)

and the number of causal variants as m (300 or 3,000). Causal variants were generated as fol-

lows: m=3causal variants were selected from A1, m=3

from A2 and the rest from (A1UA2)C corre-

sponding to a high enrichment of signals in A1 and A2. Effect sizes of causal variants were

sampled from N 0;h2gm

� �. For each simulation, we used 70% of the data to calculate the training

summary statistics and randomly divided the rest 30% into two parts for parameter tuning.

We also randomly selected half of the training data to calculate summary statistics in order to

study the effect of sample size on prediction accuracy.

In order to evaluate the improvement in accuracy, we performed a permutation test to

compare the CORs of AnnoPred and LDpred. Suppose the CORs of LDpred and AnnoPred in

simulations are x1, x2, . . ., xn and y1, y2, . . ., yn, respectively. And the hypothesis we want to test

is

H0 : mx ¼ my $ H1 : mx 6¼ my

where μx and μy represent the population mean of accuracies of LDpred and AnnoPred. We

used j�x � �yj as the test statistics and the p value can be calculated as p ¼ Prðj�x � �yÞ > j�xobs�

�yobsjjH0Þ, in which �x � �y represents the random variable and �xobs � �yobs represents the actually

observed values. We used permutation to approximate the distribution of ð�x � �yÞ when H0 is

true. Specifically, we first pooled xi0s and yi0s together. Then ~x1; ~x2; . . . ; ~xn and ~y1; ~y2; . . . ; ~yn

were sampled from the pooled data for N = 106 times and we calculated ð�~x � �~y Þ for each

~xi0s and ~yi

0s sampled, which formed the empirical distribution of ð�x � �yÞ under H0. And the

p value could be approximated by p ¼PN

k¼1Ifj�~x k � �~y kj>j�xobs� �yobs jg

N , in which �~x k ��~y k represents the

sampled test statistic of the kth permutation.



https://github.com/bvilhjal/ldpred

https://github.com/bvilhjal/ldpred


To further study the effect of sample size on prediction performance, we simulated traits

using SNPs of chromosome 1, chromosomes 1 and 2, chromosomes 1 to 4 and the whole

genome while keeping the same proportion of causal variants and heritability to mimic the sit-

uation of increasing sample size. The corresponding relative sample sizes (N MMs

, where N is the

number of individuals, M is the total number of variants and Ms is the number of variants used

in simulation) for the four scenarios are ~135K, ~67K, 37K and ~11K. For each effective sam-

ple size, we simulated traits under four settings: h2 = 0.25, p = 0.001; h2 = 0.25, p = 0.01; h2 =

0.5, p = 0.001; h2 = 0.5, p = 0.01, where p represents the proportion of causal variants (Fig 1).

Ethics statement

The study was approved by YALE UNIVERSITY HUMAN INVESTIGATION COMMITTEE

with approval number 100 FR1 and 100 FR27.

Data access

GWAS summary statistics and validation data

We trained AnnoPred using publicly accessible GWAS summary statistics and evaluated risk

prediction performance using individual-level genotype and phenotype data from cohorts

independent from the training samples. Only SNPs shared between training and testing data-

sets were kept in our analyses. Details for each training and testing dataset are provided in S1

Text and S8 Table.

For Crohn’s disease, we trained the model using summary statistics from International

Inflammatory Bowel Disease Genetics Consortium (IIBDGC; Ncase = 6,333 and Ncontrol =

15,056) [25]. Samples from the Wellcome Trust Case Control Consortium (WTCCC) were

removed from the meta-analysis and used as the validation dataset (Ncase = 1,689 and Ncontrol =

2,891) [26]. For breast cancer, we trained the model using summary statistics from Genetic

Associations and Mechanisms in Oncology (GAME-ON) study (Ncase = 16,003 and Ncontrol =

41,335) [27], and tested the performance using samples from the Cancer Genetic Markers of

Susceptibility (CGEMS) study (Ncase = 966 and Ncontrol = 70) [28]. Shared samples between

CGEMS and GAME-ON were removed. We used samples from the CIDR-GWAS of breast

cancer for trans-ethnic analysis (Ncase = 1,666 and Ncontrol = 2,038) [29]. For rheumatoid arthri-

tis, we used summary statistics from a meta-analysis with 5,539 cases and 20,169 controls to

train the model [30]. WTCCC samples were removed from the meta-analysis and used for

validation (Ncase = 1,829 and Ncontrol = 2,892) [26]. For type-II diabetes, the training dataset

is Diabetes Genetics Replication and Meta-analysis (DIAGRAM) consortium GWAS with

12,171 cases and 56,862 controls [31]. We used samples from Northwestern NUgene Project for

validation (Ncase = 662 and Ncontrol = 517) [32]. Samples from Institute for Personalized Medi-

cine (IPM) eMERGE project are used for trans-ethnic analysis (African American: Ncase = 517

and Ncontrol = 213; Hispanic: Ncase = 477 and Ncontrol = 102) [33]. The training dataset for celiac

disease is from a GWAS with 4,533 cases and 10,750 controls [34]. Samples in the National

Institute of Diabetes and Digestive and Kidney Diseases (NIDDK) celiac disease study were

used for validation (Ncase = 1,716 and Ncontrol = 530) [35].

Software availability

AnnoPred software and source code are freely available online at https://github.com/

yiminghu/AnnoPred.






Supporting information

S1 Fig. Enrichment of proportion of cases in the top 5% testing samples with high PRS.

(TIFF)

S2 Fig. Boxplots of the simulation results in Table 1, p-values of the permutation tests

(Methods) quantify the improvement of AnnoPred over PRS without incorporating func-

tional annotations.

(TIFF)

S3 Fig. Heritability enrichment across GenoCanyon and tissue-specific GenoSkyline anno-

tations. The horizontal line marks no enrichment.

(TIFF)

S4 Fig. Per-SNP heritability estimation under constant enrichment in simulation. Dashed

line marks the true per-SNP heritability.

(TIFF)

S5 Fig. Proportion of SNPs in GenoCanyon and tissue-specific GenoSkyline annotations.

(TIFF)

S6 Fig. Prediction accuracy of AnnoPred on Crohn’s disease data using different LD radi-

uses.

(TIFF)

S7 Fig. Comparing signal strength of SNPs with high priors and low priors in independent

validation cohorts with underpowered sample size (<2000). (A) Breast cancer (B) Type-II

diabetes (C) Comparing consistency of SNPs’ effect direction between training and testing

datasets. Each bar quantifies the proportion of SNPs with consistent effect directions. The

association tests and effect size estimation on the testing data are underpowered due to the

limited sample size.

(TIFF)

S1 Table. GWAS signal enrichment across 61 annotation categories.

(XLSX)

S2 Table. AUCs of different methods. The highest AUCs are highlighted in boldface.

(XLSX)

S3 Table. Comparison of the complete model and AnnoPred with baseline annotations.

The highest AUCs are highlighted in boldface.

(XLSX)

S4 Table. Comparison of the AnnoPred with method used in (Speed and Balding 2014) for

evaluation in real data analysis. The highest AUCs are highlighted in boldface.

(XLSX)

S5 Table. Comparison of the AnnoPred with method used in (Speed and Balding 2014) for

evaluation in simulation. The highest correlations are highlighted in boldface.

(XLSX)

S6 Table. AUCs for trans-ethnic analyses. The highest AUCs are highlighted in boldface.

(XLSX)

S7 Table. CORs for trans-ethnic analyses. The highest CORs are highlighted in boldface.

(XLSX)



http://journals.plos.org/ploscompbiol/article/asset?unique&id=info:doi/10.1371/journal.pcbi.1005589.s001















S8 Table. URLs for training and testing datasets.

(XLSX)

S9 Table. Prediction accuracies after removing SNPs in MHC regions. The highest CORs/

AUCs are highlighted in boldface.

(XLSX)

S10 Table. Prediction accuracies of AnnoPred when different annotations used. The high-

est CORs/AUCs are highlighted in boldface.

(XLSX)

S11 Table. p-values from the likelihood ratio tests comparing different models.

(XLSX)

S12 Table. Prediction accuracies on T2D when tuning the parameter in an independent

cohort.

(XLSX)

S1 Text. Details on GWAS summary statistics and validation data.

(DOCX)

Acknowledgments

We sincerely thank DIAGRAM, GAME-ON, IIBDGC, and ImmunoBase for making their

GWAS summary data publicly accessible. This study makes use of data generated by the Well-

come Trust Case-Control Consortium. A full list of the investigators who contributed to the

generation of the data is available from www.wtccc.org.uk. Funding for the project was pro-

vided by the Wellcome Trust under award 076113, 085475 and 090355. We also thank Dr.

Bjarni J. Vilhjalmsson for sharing his codes. And finally we thank Jina Li for her insightful sug-

gestions and support.

Author Contributions

Conceptualization: YH QL HZ.

Data curation: CY.

Formal analysis: YH QL HZ.

Methodology: YH QL HZ.

Software: YH RP XY.

Validation: YH QL FF XX CY.

Writing – original draft: YH QL HZ.

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